scholarly journals Partial-limit solutions and rational solutions with parameter for the Fokas-Lenells equation

2021 ◽  
Author(s):  
Hua Wu
Keyword(s):  
Rational Solutions ◽  
Partial Limit ◽  
Limit Solutions

scholarly journals Partial-limit Solutions and Rational Solutions with Parameter for the Fokas-Lenells Equation

2021 ◽  
Author(s):  
Hua Wu
Keyword(s):  
Soliton Solutions ◽  
Rational Solutions ◽  
Intrinsic Parameter ◽  
Algebraic Decay ◽  
Partial Limit ◽  
Repeated Eigenvalues ◽  
Double Eigenvalue ◽  
Limit Procedure ◽  
Limit Solutions ◽  
Zero Phase

Abstract A partial-limit procedure is applied to soliton solutions of the Fokas-Lenells equation. Multiple-pole solutions related to real repeated eigenvalues are obtained. For the envelop | u | 2 , the simplest solution corresponds to a real double eigenvalue, showing a solitary wave with algebraic decay. Two such solitons allow elastic scattering but asymptotically with zero phase shift. Single eigenvalue with higher multiplicity gives rise to rational solutions which contain an intrinsic parameter, live on a zero background, and have slowly-changing amplitudes.

scholarly journals ON PROPERTIES OF FINITE-ORDER MEROMORPHIC SOLUTIONS OF A CERTAIN DIFFERENCE PAINLEVÉ I EQUATION

2011 ◽  
Vol 85 (3) ◽  
pp. 463-475 ◽  
Author(s):  
MEI-RU CHEN ◽  
ZONG-XUAN CHEN
Keyword(s):  
Finite Order ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
The Difference ◽  
Image Position

AbstractIn this paper, we investigate properties of finite-order transcendental meromorphic solutions, rational solutions and polynomial solutions of the difference Painlevé I equation where a, b and c are constants, ∣a∣+∣b∣≠0.

Rational solutions of the KdV equation with damping

1979 ◽  
Vol 24 (4) ◽  
pp. 97-100 ◽  
Author(s):  
F. Calogero ◽  
M. A. Olshanetsky ◽  
A. M. Perelomov
Keyword(s):  
Kdv Equation ◽  
Rational Solutions ◽  
The Kdv Equation

RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION

2008 ◽  
Vol 06 (04) ◽  
pp. 349-369 ◽  
Author(s):  
PETER A. CLARKSON
Keyword(s):  
Infinite Number ◽  
Boussinesq Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Rational Solutions ◽  
Painleve Equations ◽  
Special Polynomials ◽  
Symmetry Reductions ◽  
Nonlinear Schrodinger Equations ◽  
De Vries

Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.

Chirped and chirp-free optical solitons for Heisenberg ferromagnetic spin chains model

2021 ◽  
pp. 2150139
Author(s):  
Syed Tahir Raza Rizvi ◽  
Aly R. Seadawy ◽  
Ishrat Bibi ◽  
Muhammad Younis
Keyword(s):  
Graphical Representation ◽  
Spin Dynamics ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Optical Solitons ◽  
Spin Chains ◽  
Solitary Wave Solutions ◽  
Rational Solutions ◽  
Wave Solutions ◽  
Ode Method

In this paper, we study (2+1)-dimensional non-linear spin dynamics of Heisenberg ferromagnetic spin chains equation (HFSCE) for various soliton solutions. We obtain two types of optical solitons i.e. chirp free and chirped solitons. We obtain bright and bright-like soliton, singular-like solitons, periodic and rational solutions, Weierstrass elliptic functions solutions and other solitary wave solutions for HFSCE with the aid of sub-ODE method. At the end, we present graphical representation of our solutions.

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